Neural Trees for Learning on Graphs
- URL: http://arxiv.org/abs/2105.07264v1
- Date: Sat, 15 May 2021 17:08:20 GMT
- Title: Neural Trees for Learning on Graphs
- Authors: Rajat Talak, Siyi Hu, Lisa Peng, and Luca Carlone
- Abstract summary: Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs.
We propose a new GNN architecture -- the Neural Tree.
We show that the neural tree architecture can approximate any smooth probability distribution function over an undirected graph.
- Score: 19.05038106825347
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach
for learning over graphs. Despite this success, existing GNNs are constrained
by their local message-passing architecture and are provably limited in their
expressive power. In this work, we propose a new GNN architecture -- the Neural
Tree. The neural tree architecture does not perform message passing on the
input graph but on a tree-structured graph, called the H-tree, that is
constructed from the input graph. Nodes in the H-tree correspond to subgraphs
in the input graph, and they are reorganized in a hierarchical manner such that
a parent-node of a node in the H-tree always corresponds to a larger subgraph
in the input graph. We show that the neural tree architecture can approximate
any smooth probability distribution function over an undirected graph, as well
as emulate the junction tree algorithm. We also prove that the number of
parameters needed to achieve an $\epsilon$-approximation of the distribution
function is exponential in the treewidth of the input graph, but linear in its
size. We apply the neural tree to semi-supervised node classification in 3D
scene graphs, and show that these theoretical properties translate into
significant gains in prediction accuracy, over the more traditional GNN
architectures.
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